scholarly journals The role of physical digit representation and numerical magnitude representation in children’s multiplication fact retrieval

2016 ◽  
Vol 152 ◽  
pp. 41-53 ◽  
Author(s):  
Alice De Visscher ◽  
Marie-Pascale Noël ◽  
Bert De Smedt
Keyword(s):  
Numerical Magnitude ◽  
Magnitude Representation ◽  
Numerical Magnitude Representation ◽  
Fact Retrieval

The case for a notation-independent representation of number

2009 ◽  
Vol 32 (3-4) ◽  
pp. 333-335 ◽  
Author(s):  
Stanislas Dehaene
Keyword(s):  
Empirical Evidence ◽  
Numerical Magnitude ◽  
Subliminal Priming ◽  
Magnitude Representation ◽  
Modality Effects ◽  
Automatic Activation

AbstractCohen Kadosh & Walsh (CK&W) neglect the solid empirical evidence for a convergence of notation-specific representations onto a shared representation of numerical magnitude. Subliminal priming reveals cross-notation and cross-modality effects, contrary to CK&W's prediction that automatic activation is modality and notation-specific. Notation effects may, however, emerge in the precision, speed, automaticity, and means by which the central magnitude representation is accessed.

The role of executive functions in numerical magnitude skills

2013 ◽  
Vol 24 ◽  
pp. 145-151 ◽  
Author(s):  
Meijke E. Kolkman ◽  
Herbert J.A. Hoijtink ◽  
Evelyn H. Kroesbergen ◽  
Paul P.M. Leseman
Keyword(s):  
Executive Functions ◽  
Numerical Magnitude

The role of practice in fact retrieval.

1985 ◽  
Vol 11 (1) ◽  
pp. 136-153 ◽  
Author(s):  
Peter L. Pirolli ◽  
John R. Anderson
Keyword(s):  
Fact Retrieval

Order and Magnitude Share a Common Representation in Parietal Cortex

2009 ◽  
Vol 21 (11) ◽  
pp. 2114-2120 ◽  
Author(s):  
Michael S. Franklin ◽  
John Jonides
Keyword(s):  
Distance Effect ◽  
Number Line ◽  
Judgment Task ◽  
Mental Number Line ◽  
Numerical Magnitude ◽  
Intraparietal Sulcus ◽  
Ordinal Information ◽  
Common Representation ◽  
Distance Effects

The role of the intraparietal sulcus (IPS) in the representation of numerical magnitude is well established. Recently, there has also been speculation that the IPS is involved in the representation of ordinal information as well. These claims, however, overlook the fact that all neuroimaging paradigms in which participants make judgments about either magnitude and/or order result in a behavioral distance effect (i.e., the comparison is easier when the stimuli span a greater distance). This leaves open two possibilities: It may be that activation of the IPS is due to the mechanism that yields distance effects, or it may be that the IPS is involved in the representation of information about both magnitude and order. The current study used fMRI to compare a magnitude task in which participants show distance effects to an order-judgment task that yields reverse-distance effects. The results reveal activation of the IPS for both the magnitude and order tasks that is based on participants' strategies as opposed to the actual distance between the numbers. This leads to the conclusion that the IPS represents a mental number line, and that accessing this line can lead to distance effects when participants compare magnitudes and to reverse-distance effects when participants check for order.

scholarly journals Relational quantitative reasoning in kindergarten predicts mathematical achievement in third grade

2016 ◽  
Vol 2 (2) ◽  
pp. 77-90 ◽  
Author(s):  
Lennart Schalk ◽  
Henrik Saalbach ◽  
Roland H. Grabner ◽  
Elsbeth Stern
Keyword(s):  
Elementary School ◽  
Mathematical Achievement ◽  
Quantitative Reasoning ◽  
Third Grade ◽  
Outcome Variable ◽  
Numerical Magnitude ◽  
Long Term Effects ◽  
Domain Specific ◽  
Reading Abilities ◽  
Numerical Magnitude Representation

Tremendous variation in elementary school children’s mathematical achievement can partly be traced back to differences in early domain-specific quantitative competencies. While previous research mainly focused on numerical magnitude representation and counting, we tested the long-term effects of relational quantitative reasoning. Before children (N = 51) entered school (i.e. at age 5-6), we assessed this competence with a test that required no knowledge about Arabic numerals. Two and a half years later, when children were in third grade of elementary school, we gauged mathematical achievement, general reasoning ability, and reading skills. A multiple regression analysis with mathematical achievement as outcome variable revealed a small but unique impact of children’s relational quantitative reasoning in kindergarten on their later mathematical achievement after controlling for general reasoning and reading abilities. Thus, a considerable amount of individual differences in mathematics achievement in elementary school results from differences in early relational quantity understanding that emerge before systematic instruction starts.

Developmental Dyscalculia

2015 ◽  
Vol 223 (2) ◽  
pp. 69-82 ◽  
Author(s):  
Jörg-Tobias Kuhn
Keyword(s):  
Number Processing ◽  
Cognitive Resources ◽  
Cognitive Profiles ◽  
Developmental Dyscalculia ◽  
Hyperactivity Disorder ◽  
Magnitude Processing ◽  
Specific Learning Disorder ◽  
Behavioral Evidence ◽  
Fact Retrieval

Developmental dyscalculia (DD) is a specific learning disorder that affects the acquisition of arithmetic skills and number processing in children. A high comorbidity between DD and other neurodevelopmental disorders (e.g., dyslexia, attention-deficit/hyperactivity disorder [ADHD]) as well as substantial heterogeneity in cognitive profiles have been reported. Current studies indicate that DD is persistent, has a genetic component, and is related to functional and structural alterations of brain areas involved in magnitude representation. Recent neuronal and behavioral evidence is presented, showing that DD entails (a) impairments in two preverbal core systems of number, an approximate system for estimating larger magnitudes and an exact system for representing small magnitudes, (b) deficits in symbolic number processing, (c) aberrant and nonadaptive neuronal activation in basic magnitude processing and calculation, (d) dysfunctional arithmetic fact retrieval and persistent use of counting strategies in calculation, and (e) deficits in visuospatial working memory and the central executive. Finally, open research questions, including the role of domain-general cognitive resources in DD, causes and developmental consequences of comorbidity, as well as design and evaluation of interventions for DD, are briefly discussed.

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